Dipole nature of sound radiation by free turbulence with shear

Abstract

The theory of aerodynamic generation of sound, whose fundamental principles were expounded by Lighthill in [1, 2], is used most in studying stream noise. According to this theory, the process of sound generation by free turbulence reduces to a quadrupole radiation mechanism and the sound intensity (without taking account of the effects of refraction and convection) depends on the stream velocity to the eighth power. In later years the Lighthill theory received intensive development in various directions. In particular, a number of papers, for example [3–7], in which the radiation of sound by a free stream was represented as the superposition of “shear noise” and “intrinsic noise” of turbulent pulsations, are devoted to the questions considered here about the influence of the mean velocity shear. A deduction is made in these papers which rely on the Lighthill theory, about the identical order of the intrinsic and shear noises. At the same time, the results of a number of experiments [8, 9] on the noise of subsonic jets show that the noise intensity at low subsonic velocities is proportional to the sixth power of the stream velocity. A dependence of the noise intensity on the sixth power of the velocity has been obtained by computational means in [10, 11] without relying on the Lighthill scheme for the solution. The noise intensity of a subsonic jet for just the shear component of the radiation was computed in [10] on the basis of the general solution of the wave equation, and it has been clarified that for low Mach numbers Maxa [M≤0.5] the sixth-power law is valid. This same law has been obtained in [11] for an acoustic field produced by pairs of moving vortices by using the method of matched asymptotic expansions. An attempt to explain the sixth-power law for the noise intensity of free turbulent streams by starting from the quadrupole radiation scheme was tried in [6], where it was assumed that the velocity pulsations depend on the stream velocity to the 3/4 rather than the first power. Utilization of this argument is inadequate since a direct dimensional analysis of the Lighthill solution results in a 7.5 power-law for shear noise and a seventh power law for the intrinsic noise of turbulent pulsations. This paper is devoted to an analysis of the discrepancy between the Lighthill quadrupole character of the sound radiation and the sixth-power dependence of the sound intensity on the stream velocity obtained as a result of the mentioned calculations [10, 11] and a number of experiments.